My relatives disapprove of my BF's religion
First, awesome job on finding a guy who both you and your parents like. And kudos for being open-minded. But as you so unfortunately discovered, not everyone dismisses stereotypes so readily. Prejudice is an easy thing to find and a difficult thing to face – especially when it's coming from a family member. This advice isn't going to rid all of the world's intolerance (we wish), but hopefully it will patch up this sticky family sitch.
Open mind, open discussion
Start off with a warm and heartfelt talk. Tell her that though you respect her, you were hoping she would be more tolerant and accepting of your boyfriend and his beliefs. Calmly stand true to your principles, but more importantly, avoid any blame games or sweeping generalizations. After all, those pesky presumptions are what started this problem in the first place.
Knowledge is power
They say people fear what they do not know. Suggest discussing some of his religion's beliefs with her. If she's open to it, your aunt will find that unlike the extremists portrayed in the media, Islam promotes good will and peace. Once she understands this, she'll be able to see your guy for who he is, and not the negative stereotypes she has ingrained in her mind.
If she won't budge in taking off her bigoted blinders, don't let that bother you. Realize that those beliefs are hers – no matter how much you disagree – and put this discordance out of your minds at family get-togethers. Most importantly, remember to stick to your convictions while still being considerate of others' opinions. Your aunt might not change her mind, but maybe you'll inspire others to be more accepting.